**“Easy” questions:**

Question 1:

Find the slope of the tangent to the curve represented by the curve and at the point .

Question 2:

Find the co-ordinates of the point P on the curve , the tangent at which is perpendicular to the line .

Question 3:

Find the co-ordinates of the point lying in the first quadrant on the ellipse so that the area of the triangle formed by the tangent at P and the co-ordinate axes is the smallest.

Question 4:

The function , where is

(a) increasing on

(b) decreasing on

(c) increasing on and decreasing on

(d) decreasing on and increasing on .

Fill in the correct multiple choice. Only one of the choices is correct.

Question 5:

Find the length of a longest interval in which the function is increasing.

Question 6:

Let , then is

(a) increasing on

(b) decreasing on

(c) increasing on

(d) decreasing on .

Fill in the correct choice above. Only one choice holds true.

Question 7:

Consider the following statements S and R:

S: Both and are decreasing functions in the interval .

R: If a differentiable function decreases in the interval , then its derivative also decreases in .

Which of the following is true?

(i) Both S and R are wrong.

(ii) Both S and R are correct, but R is not the correct explanation for S.

(iii) S is correct and R is the correct explanation for S.

(iv) S is correct and R is wrong.

Indicate the correct choice. Only one choice is correct.

Question 8:

For which of the following functions on , the Lagrange’s Mean Value theorem is not applicable:

(i) , when ; and , when .

(ii) , when ; and , when .

(iii)

(iv) .

Only one choice is correct. Which one?

Question 9:

How many real roots does the equation have?

Question 10:

What is the difference between the greatest and least values of the function ?

More later,

Nalin Pithwa.